X-ray reflected spectra from accretion disk models.II. Diagnostic tools for X-ray observations

0.84 MB·English

by  J. Garcia

X-ray reflected spectra from accretion disk models.
II. Diagnostic tools for X-ray observations
J. Garc´ıa1,2, T.R. Kallman2,
1
1 and
0
2
R.F. Mushotzky3
n
a
J

5
Received ; accepted

]
E
H
.
h
p
-
o
r
t
s
a
[

1
v
5
1
1
1
.
1
0
1
1
:
v
1Department of Physics, Western Michigan University, Kalamazoo, MI 49008, USA
i
X
r [email protected]
a
2NASA Goddard Space Flight Center, Greenbelt, MD 20771
[email protected]
3Department of Astronomy, University of Maryland, College Park, MD, USA
[email protected]
– 2 –
ABSTRACT
We present a comprehensive study of the emission spectra from accreting
sources. We use our new reflection code to compute the reflected spectra from an
accretion disk illuminated by X-rays. This set of models covers different values of
ionization parameter, solar iron abundance andphoton index for the illuminating
spectrum. These models also include the most complete and recent atomic data
for the inner-shell of the iron and oxygen isonuclear sequences. We concentrate
our analysis to the 2−10 keV energy region, and in particular to the iron K-shell
emission lines. We show the dependency of the equivalent width (EW) of the Fe
Kα with the ionization parameter. The maximum value of the EW is ∼ 800 eV
for models with log ξ ∼ 1.5, and decreases monotonically as ξ increases. For
lower values of ξ the Fe Kα EW decreases to a minimum near log ξ ∼ 0.8. We
produce simulated CCD observations based on our reflection models. For low
ionized, reflection dominated cases, the 2 − 10 keV energy region shows a very
broad, curving continuum that cannot be represented by a simple power-law.
We show that in addition to the Fe K-shell emission, there are other prominent
features such as the Si and S Lα lines, a blend of Ar viii-xi lines, and the Ca x
Kα line. In some cases the S xv blends with the He-like Si RRC producing a
broadfeaturethat cannot bereproduced bya simple Gaussianprofile. This could
be used as a signature of reflection.
1. Introduction
Accreting systems are observed to emit copious radiation in the X-ray energy range
which suggests emission from the innermost regions of an accretion disk. Analysis of the
– 3 –
X-ray spectra is crucial to study the complex mixture of emitting and absorbing components
in the circumnuclear regions of these systems. However, there are only few observables that
provide indication of the existence of an accretion disk. These need to be understood in
order to correctly interpret the physics of these systems. In a general sense, the observed
radiation from accreting sources can be divided into: a thermal component, in the form of a
black body emitted at the surface of the disk with typical temperatures of ∼ 0.01−10 keV
(for the mass range ∼ 108 − 10 M ); a coronal component in the form of a power law
⊙
covering energies up to ∼ 100 keV, believed to arise from inverse Compton scattering in a
hot gas that lies above the disk; and a reflected component, resulting from the interaction
of some of the coronal X-ray photons and the optically thick material of the disk. In the
reflected component, the most prominent feature is the iron Kα emission line at ∼ 6.4 keV,
produced by transitions of electrons between the 1s and 2p atomic orbitals. These are
ubiquitous in the spectra of accreting sources (Pounds et al. 1990; Nandra & Pounds 1994;
Miller 2007). Other reflection signatures are the so called Compton shoulder (next to the
Fe K-line), and the Compton hump (above ∼ 10 keV), produced by the down-scattering of
high energy photons by cold electrons.
Much theoretical effort has gone into studies of X-ray illuminated disks over the
past few decades. Most models assume that the gas density is constant with depth
(Done et al. 1992; Ross & Fabian 1993; Matt et al. 1993; Czerny & Zycki 1994; Krolik et al.
1994; Magdziarz & Zdziarski 1995; Ross et al. 1996; Matt et al. 1996; Poutanen et al.
1996; Blackman 1999). Although constant density models may be appropriate for
radiation-pressure dominated disks, other studies have shown significant differences when
the gas density is properly solved via hydrostatic equilibrium (Rozanska & Czerny 1996;
Nayakshin et al. 2000; Nayakshin & Kallman 2001; Ballantyne et al. 2001; Dumont et al.
2002; Ross & Fabian 2007). Recently we have developed a new model for the reflected
spectra fromilluminatedaccretiondiskscalledxillver(Garc´ıa & Kallman2010). Although
– 4 –
our code is similar in its principal assumptions to previous models, xillver includes the
most recent and complete atomic data for K-shell of all relevant ions (Kallman et al. 2004;
Garc´ıa et al. 2005; Palmeri et al. 2008; Garc´ıa et al. 2009; Palmeri et al. 2010). This has a
dramatic impact on the predicted spectra, in particular the Kα emission from iron. With
this model we can study the effects of incident X-rays on the surface of the accretion disk
by solving simultaneously the equations of radiative transfer and ionization equilibrium
over a large range of column densities. Plane-parallel geometry and azimuthal symmetry
are assumed, such that each calculation corresponds to an annular ring at a given distance
from the source of X-rays. The redistribution of photons due to Compton down-scattering
is included by using a Gaussian approximation for the Compton kernel. With xillver we
are able to solve the reflection problem with great detail, i.e., with very high energy, spatial
and angular resolution.
In this paper we present a systematic analysis of our models for reflected spectra from
X-ray illuminated accretion disks. We show how the most relevant atomic features in the
spectra depend on the assumed properties of the irradiated gas. We pay particular attention
to the Fe K-shell emission lines, and we quantify its strength in terms of the equivalent
widths predicted by our models. These models are also used to produce faked CCD spectra
in order to simulate the effects of the instrumental response and limited spectral resolution.
These results will be helpful diagnostic tools in the interpretation of accreting sources
observations.
In the next Section we describe briefly the numerical methods used in our reflection
code. In Section 3 we present the results of our analysis on the simulated spectra, as well
as comparisons with observations from Seyfert galaxies and X-ray binaries. The main
conclusions are presented in Section 4
– 5 –
2. The Reflection Model
In order to calculate the reflected spectra from X-ray illuminated accretion disks we
make use of our reflection code xillver. The details of the calculations are fully described
in Garc´ıa & Kallman (2010), thus here we just review the main aspects.
The description of the interaction of the radiation with the gas in the illuminated slab
requires the solution of the transfer equation:
∂2u(µ,E,τ) ∂ω(E,τ)∂u(µ,E,τ)
µ2ω2(E,τ) +µ2ω(E,τ) = u(µ,E,τ)−S(E,τ) (1)
∂τ2 ∂τ ∂τ
where u(µ,E,τ) is the average intensity of the radiation field for a given cosine of the
angle with respect to the normal µ, energy E, and position in the slab, specified by the
Thomson optical depth dτ ≡ −α dz = −σ n dz, where σ is the Thomson cross section
T T e T
(= 6.65× 10−25 cm2), and n is the electron number density. The quantity ω is defined
e
as the ratio of the Thomson scattering coefficient α to the total opacity χ(τ,E). The
T
second term in the right-hand side of Equation 1 is the source function, which is defined as
the ratio of the total emissivity over the total opacity of the gas, taking into account both
scattering and absorption processes:
α (E) j(E,τ)
kn
S(E,τ) = J (E,τ)+ (2)
c
χ(E,τ) χ(E,τ)
where α (E) is the Klein-Nishina scattering coefficient, j(E,τ) is the thermal continuum
kn
plus lines emissivity, and J (E,τ) is the Comptonized mean intensity, given by the Gaussian
c
convolution
1 ∞ −(E −E )2 1
′ c ′
J (E,τ) = dE exp u(µ,E ,τ)dµ (3)
c σπ1/2 Z (cid:20) σ2 (cid:21)Z
0 0
The Gaussian is centered at E = E′(1 +4θ −E′/m c2), where m is the electron mass,
c e e
c is the speed of light, and θ = kT/m c2 is the dimensionless temperature. The energy
e
dispersion is given by σ = E′ 2θ+ 2(E′/m c2)2 1/2.
5 e
(cid:2) (cid:3)
– 6 –
The solution of the system is completed by imposing two boundary conditions. At the
top of the slab (τ = 0), we specify the incoming radiation field incident at a given angle µ
0
by
∂u(τ,µ,E) 2F (E)
ω(0,E)µ −u(0,µ,E) = − x δ(µ−µ ) (4)
0
(cid:20) ∂τ (cid:21) µ
0 0
where F (E) is the net flux of the illuminating radiation incident at the top of the slab.
x
At the inner boundary (τ = τ ), we specify the outgoing radiation field to be equal to a
max
blackbody with the expected temperature for the disk:
∂u(τ,µ,E)
ω(τ ,µ,E)µ +u(τ ,µ,E) = B(T ) (5)
max max disk
(cid:20) ∂τ (cid:21)
τmax
where T can be defined using the Shakura & Sunyaev (1973) formulae. Since these
disk
models are calculated under the assumption of constant density, we use the common
definition of the ionization parameter (Tarter et al. 1969) to characterize each case:
4πF
x
ξ = . (6)
n
e
where n is the electron gas density, and F is the net illuminating flux integrated in the
e x
1 − 1000 Ry energy range. The solution of the system is found by forward elimination
and back substitution. A full transfer solution must be achieved iteratively in order to
self-consistently treat the scattering process. This procedure requires ∼ τ2 iterations
max
(lambda iterations) for convergence.
Given the solution for the radiation field at each point in the atmosphere, we use
the photoionization code xstar (Kallman & Bautista 2001) to determine the state of the
gas at each point of the gas. The state of the gas is defined by its temperature and the
level populations of the ions. The relative abundances of the ions of a given element and
the level populations are found by solving the ionization equilibrium equations under the
assumption of local balance, subject to the constraint of particle number conservation for
each element. xstar calculates level populations, temperature, the opacity χ(E,τ) and the
– 7 –
total emissivity j(E,τ) of the gas assuming that all the physical processes are in steady
state and imposing radiative equilibrium.
The xstar atomic database collects recent data from many sources including CHIANTI
(Landi & Phillips 2006), ADAS (Summers 2004), NIST (Ralchenko et al. 2008), TOPbase
(Cunto et al. 1993) and the IRON project (Hummer et al. 1993). The database is described
in detail by Bautista & Kallman (2001). Additionally, the atomic data associated with
the K-shell of the Fe ions incorporated in the current version of xstar has been recently
calculated and represents the most accurate and complete set available to the present. A
compilation of these results and a careful study of their impact on the photoionization
models can be found in Kallman et al. (2004). Moreover, xstar also includes the atomic
data relevant to the photoabsorption near the K edge of all oxygen (Garc´ıa et al. 2005),
and nitrogen ions (Garc´ıa et al. 2009).
Finally, all the calculations presented in this paper were carried out over a large optical
depth (τ = 10), considering high resolution spectra with an energy grid of at least 5×103
max
points (R = E/∆E ∼ 350), 200 spatial zones, and 50 angles to account for anisotropy of
the radiation field. The simulations do not take into account the dynamics of the system.
Input parameters common to all these models are: the electron gas density n = 1015 cm−3,
e
photon index of the incident radiation Γ = 2, mass of the central object M = 108 M ,
⊙
distance from the central object R = 7R , and the mass accretion rate M˙ = 1.6×10−3M˙ ,
s Edd
where R = 2GM/c2 is the Schwarzschild radius and M˙ is the accretion rate at the
s Edd
Eddington limit. This particular set of parameters yields a disk effective temperature of
T = 2.8×104 ◦K. The models presented here cover 10 different values for the illumination
disk
flux F = 5×1014 −5×1017 erg cm−2 s−1, which corresponds to ionization parameters of
x
log ξ = 0.8,1.1,1.5,1.8,2.1,...,3.8. It is important to notice that these simulations are not
constrained to a particular geometry for the illumination. This is because the flux F of the
x
– 8 –
illuminating radiation is defined at the surface of the slab, regardless of the position of the
X-ray source. Therefore, a set of models with different values of the ionization parameter
can be used to construct a particular geometry, by defining the luminosity and location
of the source. We do not consider models with ionization parameters lower than ∼ 4π
(log ξ = 0.8), since our code is optimized for calculations of medium to high ionization.
The upper limit is set to log ξ = 3.8, because at such a high illumination the gas is almost
completely ionized over a large depth.
3. Results
3.1. Equivalent Widths
The equivalent width of a line provides a quantitative measure of the strength of the
spectral profile, both in emission or absorption. It is defined by the well known formula
Ehigh (F(E)−F (E))
c
EW = dE, (7)
Z F (E)
Elow c
where F(E) is the total flux and F (E) is the total flux of the continuum under the line.
c
The integration is performed over the energy range where the spectral feature takes place,
between E and E . Usually, there are uncertainties in the determination of the
low high
intrinsic continuum which affects the knowledge of the integration region and the actual
value of the equivalent width itself. Nonetheless, one can approximate its calculation by
defining an energy region in which one knows only the spectral feature of interest appears,
and where a local continuum can be defined.
In this paper we make use of the equivalent width as a measure of the strength of
several features in the X-ray spectra reflected from illuminated accretion disk. As an
example, in Figure 1 we show the reflected spectra from 3 different models calculated for
log ξ = 0.8,1.8 and 2.8 in the 4-9 keV energy region, where the only atomic features are
– 9 –
due to inner-shell transitions from Fe ions. The spectra (flux vs. energy) are shown as
solid lines. Vertical dotted lines are placed at 5.5 keV and 7 keV, defining a particular
integration region. The continuum is defined as a straight line that passes through these
two points in the spectra, which is shown as dashed lines. It is clear from the Figure that
the resulting continuum does a good job reproducing the local continuum and that it is not
superimposed over any part of the emission profile. The upper limit E = 7 keV was
high
chosen such that only emission from Kα transitions of Fe are taken into account, neglecting
any Kβ emission (which occurs at energies above 7 keV). The lower limit, however, is more
arbitrary. It needs to be chosen such that all the line profile is included in the integration.
If E is set too large, part of the line emission can fall outside the range, especially for
low
cases with large values of the ionization parameter, where Comptonization smears the line
profile due to the down-scattering. However, if E is set to a small value, all the line
low
emission is taken into account but the local continuum is modified to a point that could
either under- or over-estimate the strength of the line. Therefore, we have repeated the
calculation of the equivalent widths for E = 5,5.5 and 6 keV, in order to evaluate the
low
sensitivity of the results on this lower limit.
Figure 2 shows the resulting equivalent widths as a function of the ionization parameter,
calculated for the Fe Kα emission profile in 10 of our models. Circles connected with solid
lines correspond to the integration range 5-7 keV, squares connected with dashed lines to
5.5-7 keV, and triangles connected with short-dashed lines to the integration performed
over the 6-7 keV energy range. It is clear from the Figure that the equivalent widths are
almost unaffected by the variations of the lower boundary of the integration range, with
the exception of those models with 1.5 <log ξ < 2.5. These are the most sensitive cases
probably because of the complexity of the iron K emission. For lower values of the ionization
parameter, the emission mainly occurs at 6.4 keV due to mostly neutral Fe ions. Higher
values of ξ means that the gas is highly ionized and thus mostly He- and H-like Fe ions are
– 10 –
responsible for the emission at ∼ 6.9 keV. In both cases the line profile is simple in the
sense that the emission is concentrated at one particular energy. In between, emission from
many different ions takes place at the same time, creating a more complex spectral feature,
as can be seen in the spectrum for log ξ = 1.8 in Figure 1. Since there is no clear reason
to choose one of these values of E , we choose the intermediate one (E = 5.5 keV). We
low low
consider the uncertainties in the equivalent widths to be of order of the differences between
the values shown in Figure 2 (≤ 100 eV).
Figure 3 shows a comparison of the Fe Kα equivalent widths predicted by our models
(circles connected with dashed lines), and those predicted by the models included in
reflion (triangles connected with solid lines, Ross & Fabian 2005). The calculation of
the equivalent widths is the same in both models, with the integration performed in the
5.5-7 keV energy range. There are important differences to notice in this comparison. It is
convenient to make the distinction between two regions in the plot; the region for models
with log ξ > 1.5 and the one for models with log ξ < 1.5. In the high ionization region, both
sets of models show a similar behavior, the equivalent widths decrease monotonically as
the ionization parameter increases, resembling the Baldwin effect for X-rays. Nevertheless,
in this region all our models systematically predict stronger Fe Kα emission. For those
models in the low ionization region (log ξ < 1.5), the differences are significantly larger.
In fact, reflion models predict that the equivalent widths keep growing as the ionization
parameter decreases, while our models show the opposite trend. This turn over in the values
of the equivalent widths can be understood by looking the ionization balance in detail.
Kallman et al. (2004) performed similar calculations in photoionized models using the same
atomic data used in our models. Using a set of xstar models of thin spherical shells
illuminated by the same power law spectrum they calculated the ratio of the emissivity per
particle for K line production as a function of the ionization parameter. Their Figure 7
shows the contribution of each ion of iron summing over the K lines for each one. The overall